{
  "id": "1910.01311",
  "version": "v1",
  "published": "2019-10-03T05:44:58.000Z",
  "updated": "2019-10-03T05:44:58.000Z",
  "title": "Adaptive IGAFEM with optimal convergence rates: T-splines",
  "authors": [
    "Gregor Gantner",
    "Dirk Praetorius"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1701.07764",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of [Morgenstern, Peterseim, Comput. Aided Geom. Design 34 (2015)] in 2D resp. [Morgenstern, SIAM J. Numer. Anal. 54 (2016)] in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (resp. the sum of energy error plus data oscillations) with optimal algebraic rates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-03T05:44:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal convergence rates",
      "adaptive igafem",
      "energy error plus data oscillations",
      "error estimator",
      "second-order partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}